§0arir  b ^ec0mnieiil)  a Staatarlj  (iaage 

FOR 

BOLTS,  NUTS,  AND  SCREW-THREADS, 

• i , ‘ 

^ FOR  THE  , 

UNITED  STATES  NAVY, 

INI  A Y , 18  6 8. 


WASHINGTON: 

GOVERNMENT  PRINTING  OFFICE. 
1868. 


yWlflLD  STiTIS 
STANDARD  NUT  CO. 


Manufacturers  of 

UNFINISHED,  SEMI-FINISHED  AND 
FINISHED  CASE-HARDENED 


With  U.  S.  Standard  Threads, 


ISTo.  4r7  Kingston  Street, 

BOSTON,  MASS. 

G-KO.  H.  ITOX,  J^^ent  & Treas. 


UNFINISHED  NUTS. 

For  Bolts,  1|  in.  & larger,  20  cts.  pr.  lb. 


“ 

“ If 

“ & smaller  than  1|,  18  ‘ 

‘ “ ‘ 

“ 

a 

•1 

( ( a 

“ If,  17  ‘ 

k Hi 

“ 

“ i 

Xr  9 
^ 16’ 

18  ‘ 

‘ “ 

“ 

“ X-  U- 

^ g, 

20 

1 ‘ ‘ ' 

“ 

& 1%, 

25  •' 

, a i i 

“ 

“ i 

“ 

30  “ 

i ki  a 

SEMI-FINISHED  NUTS. 

These  Nuts  are  tapped  and  laced  true  on  the  bottom. 

For  Bolt,  1 inch  & lai-ger,  25  cts.  per  lb. 

“ “ 1 in.  & larger  than  i,  28  “ “ “ 

“ “ h & tV  “ “ “ 

“ “ I & in.  40  “ “ “ 

“ “ i in.  50  “ “ “ 


The  dimensions  of  the  unfinished  and  semi-finished 
Nuts  are  the  same  as  the  finished  Nuts.  Parties 
wishing  Nuts  to  finish  loill  so  state,  arid  they  will 
he  furnished  of  the  jmoper  dimensif^is. 


FINISHED  NUTS. 

These  Nuts  are  finished  in  a 
superior  manner  by  improved  gj at ent 
machinery,  and  case-hardened.  The 
thread  and  oidside  of  every  Nut 
are  made  to  an  accurate  gauge  and 
to  the  standard  adopted  by  the  U. 
S.  Government. 


Tor 
! Bolt. 

TMck- 

ness. 

Diam- 

eter. 

No.  of 
Tk’ds. 

Price 

Each. 

j 3 in. 

3 in. 

5.00 

21- 

2f 

4i 

4 

'4.00“ 

H 

2J 

4 

n 

2^ 

~2.¥5 

\ 2 

2 

H 

' H " 

'd.50~ 

lKZ 

* 4 

2i 

5 

T.ooi’ 

i 

If 

.80 

1 u 

2f 

T 

.G5 

If 

If 

0_9_ 

1 6 

G 

.55 

li 

1? 

‘ 2 

7 

.45 

H 

If 

Hi 

7 

.35 

i 1 

1 

If 

8 

“30 

i 

T~ 

.22 

a 

4 

3 

4 

H 

Td^ 

.18 

! . J 

f 

1 ] 

‘T6^ 

11 

“15“ 

9 

1 T6 

A 

a 1 

~vr 

.12 

i ^ 

i 

i 

13 

' .To" 

I tV 

tV 

2A 

14“ 

“Too" 

; 51 

8 

I 

) 1 

T6 

~u~ 

.08 

5 

T6 

tV 

1 9 

~\H~~ 

""T07‘ 

li.,  _ 

i 

1 

To“ 

“T(Tg" 

Nuts  \ thicker,  l.'i  per  cent  additional. 
Nuts  \ thinner,  15  per  cent  less. 

Check  Nuts  (Hat  both  sides)  same  di- 
mensions and  price  as  thin  Nuts. 


II,  §, 


€0‘ 


FORM  OF  THREAD. 

Flat  top  and  bottom,  J of  pitch. 


A^ll  IVvit.s  of  o\ix*  iiiaiixiftiotiire  lire  forg:ecl,  (not  pxiiielietl,) 
"*  from  tlio  Ixcst  <i\iiility  of  ix*on. 


REPORT 


OF 


BOARD  TO  RECOMMEND  A STANDARD  GAUGE 

FOR 

BOLTS,  NUTS,  AND  SCREW-THREADS, 


FOR  THE 


UNITED  STATES  NAVY, 


MAY,  1 8 6 8. 


WASHINGTON: 

GOVERNMENT  PRINTING  OFFICE. 
1868. 


I 


■ A* 


Digitized  by  the  Internet  Archive 
in  2017  with  funding  from 

University  of  Illinois  Urbana-Champaign  Alternates 


https://archlve.org/detalls/reportofboardtorOOunit 


fc2./.  ?2/ 
Ai , A)Aj 


a> 

c 

< 


rv. 


APPROVAL  OF  DEPARTMENT  AND  BUREAU. 


Navy  Department,  Bureau  of  Steam  Engineering, 

May  15,  1868. 

Sir  : I have  the  honor  to  herewith  submit  to  the  department  for 
its  action,  the  report  of  the  Board  of  Naval  Engineers  on  a “standard 
gauge  for  bolts,  nuts,  and  screw-threads  for  the  United  States  navy,^’ 
and  to  recommend  that  its  determinations  be  accepted  as  the  navy 
standard,  and  that  directions  be  issued  to  the  various  navy  yards  to 
govern  their  practice  accordingly. 

I have  carefully  examined  the  report  and  fully  agree  with  its  con- 
clusions. Nor  can  I take  leave  of  it  without  expressing  my  great 
admiration  of  the  thoroughly  scientific  and  practical  manner  in  which 
the  subject  is  treated. 

I respectfully  recommend  that  the  report  be  printed  for  distribu- 
tion to  the  navy  yards  and  naval  steamers. 

Very  respectfully, 


B.  F.  ISHERWOOD, 

Chief  of  Bureau, 


Hon.  Gideon  Welles, 

Secretary  of  the  Bavy. 


Navy  Department,  May  16,  1868. 
Sir  : The  standard  for  the  dimensions  of  bolts  and  nuts,  as  deter - 
“^mined  by  the  board,  is,  upon  your  recommendation,  authorized  for 
the  naval  service. 


GIDEON  WELLES, 
Secretary  of  the  Navy. 
Chief  Engineer  B.  F.  Isherwood,  U.  S.  N., 

Chief  of  the  Bureau  of  Steam  Engineering, 


I' 


REPORT  OF  THE  BOARD. 


Philadelphia,  Pa.,  May  9,  1868. 

Sir  : The  board  created  by  the  Secretary's  order  of  the  28th  of 
March,  and  instructed  to  visit  the  establishments  of  the  principal  tool 
makers  and  machinery  builders  in  Boston  and  Springfield,  Massachu- 
setts ; Providence,  Rhode  Island  ; New  York  city  ; Newark,  New 
Jersey;  and  Philadelphia  and  Pittsburg,  Pennsylvania;  to  obtain  infor- 
mation in  regard  to  the  present  practice  in  the  manufacture  of  bolts 
and' nuts,  and  to  the  relative  merits  of  difiereDt  systems  of  the  same, 
with  a view  to  recommending  a standard  gauge  foP  the  navy,  has 
performed  the  duty  ask'igned  it.  The  Board  believing  it  desirable 
and  important  to  extend  the  inquiry  over  as  wide  a range  as  practi- 
cable, also  addressed  a circular  letter  explaining  the  object  of  the 
investigation  and  asking  for  information,  to  the  proprietors  of  all 
establishments  known  to  its  members,  in  localities  not  named  in 
the  order. 

To  this  letter  replies  were  received,  containing  information  and 
suggestions  of  material  importance,  which  are  embodied  in  the  fol- 
lowing report. 

In  any  system  of  bolts  and  nuts,  the  prominent  features,  in  the 
order  of  their  relative  importance,  are  as  follows: 

I.  Pitch  of  the  screw-thread,  or  number  of  threads  per  inch. 

II.  Form  and  dimensions  of  the  screw-thread. 

III.  Dimensions  of  the  nuts. 

IV.  Dimensions  of  the  bolt-heads. 

I. — Pitch  of  the  screw-thread. 

The  first  requirement  of  a screw-thread  is  that  its  inclination  shall 
be  such  that  the  component  of  the  pressure  upon  the  thread  surface, 
acting  parallel  to  the  inclined  surface  of  the  thread,  shall  be  less  than 
the  friction  between  the  thread  surfaces,  and  between  the  bottom  of 
the  nut  and  the  surface  upon  which  it  rests,  so  that  the  nut'  may  not 
run  off  under  the  influence  of  the  strain  upon  the  bolt.  If  this  con- 
dition, simply,  were  satisfied,  the  depth  of  the  thread,  which  in  any 


6 


system  must  be  a direct  function  of  the  pitch,  would  become  so 
excessive  as  to  unnecessarily  weaken  the  bolt,  by  reducing  its  effect- 
ive resisting  section.  Moreover,  the  ratio  of  the  force  applied  to  the 
wrench,  to  the  resulting  tensional  strain  upon  the  bolt,  would  be  so 
far  increased  that  the  bolt  would  twist  off  long  before  a proper  tensile 
strain  could  be  brought  upon  it. 

Practically,  the  condition  to  be  satisfied  is  that  the  pitch  of  the 
thread  shall  be  such  that  the  tendencies  of  the  bolt  to  yield  to 
tensional  and  torsional  strains  are  about  equal.  It  is  clear,  how- 
ever, that  if  this  condition  were  satisfied  in  the  case  of  new  bolts, 
having  smooth  and  well  lubricated  thread  surfaces,  there  would  still 
be  an  undue  tendency  of  the  bolt  to  yield  to  torsional  strain  in  con- 
sequence of  increased  friction  resulting  from  rust,  dirt,  abrasion  of 
surfaces  and  increased  viscidity  of  the  lubricant.  A considerable 
margin  should  therefore  be  allowed,  if  practicable,  to  cover  this 
contingency. 

Fortunately,  however,  the  necessity  for  a determination  of  the 
proportions  which  satisfy  the  requisite  condition,  based  upon  a priori 
considerations,  does  not  exist;  for  experience,  which  is  generally  the 
best  guide  in  such  matters,  has  already  fixed  the  limits  between  which 
the  system  to  be  recommended  must  be  found. 

We  find  but  two  systems  in  general  use — one  known  as  Whit- 
worth’s, deduced  many  years  ago  from  the  general  practice  of  Eng- 
lish mechanics,  and  the  other  known  as  that  of  Mr.  William  Sellers, 
deduced  more  recently  from  the  practice  of  American  mechanics. 
Beside  these,  a system  has  been  proposed  by  Kobert  Briggs,  Esq., 
Superintendent  of  the  Pascal  Iron  Works  of  this  city,  where  the 
system  has  been  adopted. 

Mr.  Briggs’s  system  does  not  dijBfer  essentially  in  respect  to  pitch, 
so  far  as  it  is  proposed  to  extend  it,  from  the  systems  of  Whitworth 
or  Sellers.  Its  peculiar  feature  will  be  noticed  further  on.  The 
following  table  (I)  exhibits  the  practice  of  our  mechanics,  so  far  as 
we  have  been  able  to  visit  or  communicate  with  them,  and  it  may  be 
presumed  that  the  average  practice  of  the  entire  country  is  fairly 
represented  by  it. 

It  will  be  observed  that  of  the  establishments  whose  practice  is 
embraced  in  the  table,  more  than  half  have  adopted  either  Whit- 
worth’s or  Sellers’s  pitches,  while  the  others  use  pitches  which,  though 
generally  not  differing  materially  from  either,  do  not  conform  to  or 
seem  to  be  based  upon  any  system  whatever. 

In  order  to  exhibit  more  clearly  the  peculiarities  of  the  different 


i 

% 


'Uto 


r/.) 


130 


i‘l5 


■mo 


OIJ 


030 


():>.} 


()0(t 


-S  -S 


> 


1 


7 


systems,  and  of  the  more  marked  deviations  from  them,  the  diagrams 
of  Plate  I have  been  prepared. 

The  abscissas  of  the  curves  represent  the  circumferences  of  the 
different  sized  bolts,  whose  diameters  are  figured  at  their  termini, 
while  the  ordinates  represent  the  corresponding  pitches.  The  cir- 
cumferences are  draw^i  full  size,  while  the  ordinates  are  magnified 
twenty  times. 


Table  I. — Representing  the  number  of  screw-threads  per  mch  on  holts  of  differerit  sizes  in  the  systems  of  Whitworth^  Sellers,  and 
Briggs;  together  with  the  numbers  used  in  the  practice  of  various  screw-bolt  manufacturers  and  machinery  builders  in  the  United 
States. 


8 


(•raa;g^s  s.sSSug 

'a)  ‘sasija  iJaqoa 


OQocoiOT}<c»<Noo>a)t^t^cocoio 


•SSBJ\[  ‘ja^seojo  M 
'•00  ouiSag;  ra'Be^g  Avaj^ 


oo500QOt^t'-«oInio 


•Biqd^apBnqd;  ‘sttog  ^ qoiuaH 


Cqifflr}<MOJr-IOO>QOt^t^O«OOin 


•pjBi  /Cab^i  BiqdiapBnqa 

OODCO^CO^r-iOOiOOI^t-COtOlOlO 

•pjBi  if  ABij  uo;soa 

20 

18 

16 

14 

13 

12 

11 

10 

9 

8 

7 

1 ® 

6 

5i 

5 

•no^sog  ‘^uBAa:>jn;g  -g 

•ifnBdcaoo  'J?  qtJOMTB  A\ 

20 

18 

16 

14 

13 

12 

11 

10 

9 

8 

7 

7 

7 

6 

6 

5 

•uoisoa 

‘iCtredmoo  P'BojpBg  uja^sBa 

•8SBJ\[ 

‘oSaAiBO  ‘8qJ0j\i  uoap  saray 

20 

18 

16  i 

14 

13 

12 

11 

10 

9 

8 

7 

7 

6 

6 

5i 

5 

•ssBpi  ‘ja:jsapjoA\.  ‘pnog  'h  ‘T 

20 

18 

16 

14 

13 

12 

11 

10 

9 

8 

7 

7 

e 

5i 

5 

•A  -N 

‘ifnBq^V  ‘nosqoBp  ^ puasnAvo  j, 

I a 

‘aonapiAOjg  ‘djuqg  uMOjg 

•unoo 

‘naABH  ^9N;  ‘meg  'V  ^ ’’3. 

OOOCO-^COC^-^OCiCXDt-t^COCoIom 

C-irHr-frHi-Hr-JrHi— 1 

T K 

‘q-iBAvaNj  ‘’oo  auiqoBi\[  Pino£) 

OOOCOTt*COC^r-*OOOOt^t^CO?OlOV^^ 

"BTqdiapB 

■Iiqa  ‘sqJOAV  joiiog  nosujBH 

OGOCO'^CO(^rHOOiaDl>i>CO<DlOLO 

C^r-HT-lrHr-l.-HrHrH 

•Biqdpp 

■■^ina  ‘Ajaq^noo;  ^ ^naraag 

20 

18 

16 

14 

13 

12 

11 

10 

9 

8 

7 

7 

6 

6 

'5i 

5 

"Biqd 

-PP^nqa  “OO  V SJapag  -tnAV 

OGOcoTPCOOJi-HOOiOOi^t^coooir^ 

•piBA  if  AB^i  q|noins:jJog 

20 

18 

16  ' 

14 

12 

12 

11 

10 

9 

8 

7 

7 

6 

6 

5 

5 

•Sjnqs^qg  ‘sAvaq^^BH  cy  pooAV 

OGO<OTj^Oi(?trHOa500t-r^CDO»0  0 

•ifaBdraoo  '^^og  3jnqs;qg 

20 

18 

]6 

14 

12 

12 

11 

10 

9 

8 

7 

7 

6 

6 

5 

5 

'sqjoAY  nog 

no^uoog  ‘‘oo  ^ pjog  ‘japng 

20 

18 

16 

14 

12 

12 

11 

10 

9 

8 

7 

7 

6 : 

6 

5 

5 1 

•ifuBduioo  aniqoBH  uo|S*g 

14 

14 

12 

11 

10 

9 

8 

7 

7 

6 

6 

6 

6 

•qaoA  Ai.a^ 

‘sqjoAi  noai  Boig  puB  nBSjoj\[ 

0000*^0?  ir-lOO>OOr>*l^COCDlOO 

Ci  r-l  rH  r-<  t-H  . r-(  .-1 

q)jBA  if  ABjq  Uifjqoojg 

•q:jjOAi;iqAi  qdasof 

ooo?OTf<oi  Ir-joo^ooi^^*cocoir5o 

r-H  .-H  1-1  f-H  . rH  rH 

0 . 

.§3 


’S  '-I 

s ^ 

I" 


a tc  fl  to  o to  a a a a 


lo  0*0  -(Cl  05 


IJ  inch 


9 


Table  I. — Representing  the  number  of  screw  threads  per  inch  on  holts  of  different  sizes,  Sfc. — Continued. 


10 


gs 

‘no^sog;  ;8Ba  ‘s^tJOAV 

20 

18 

16 

14 

13 

12 

11 

10 

9 

8 

7 

7 

6 

6 

5i 

5 

5 

4i 

3 X 

•f -N 

‘jIiBMGij;  ‘sdiinqu  ^ saAian 

'Xioi  's5[J0Ai.  QJreilV 

! 

tH  • 

I I o>  a>  oj  05  05  , 

: : rHr;oio»c^  Cl  -j:; 

M jQOOOt'-l'CO<0«OCO«5«5kdlO 

MONGREL  SYSTEMS. 

•pjojpBH  ‘-^nsd 
•raoo  suuB-aai  j;  s.^noQ 

22&20 

20&18 

18&16 

16&  14 

14&13 

12 

12&11 

12&  10 

10 

10 

10 

9 

8 

8 

•SSBJV 

‘najjBM  ‘.^aiqis  ^ saiMoua; 

18 

18 

16 

16‘ 

16 

14 

14 

12 

10 

10 

9 

8 

8 

8 

8 

8 

7 

7 

•BtqdppBpq,! 

‘gqjoM  8Ai|oraoooT;  uiAvpiBg 

00 

22 

18 

14 

10 

10 

10 

10 

10&8 

8 

8 

8 

8 

8 

8 

•ajotni; 

•{Ba  ‘XuBdxnoo  ^ isanqaizBH 

20 

20 

14i 

14i 

14i 

14.5 

12.2 

10.5 

10.5 

8.  66 

8.  66 

8 

7. 57 

7.57 

7.57 

6.66 

6.66 

5 

•ssBi\[  ‘ja^j 

-saojOjVi  ‘naoH  njnqqgBM 

20 

16 

14 

14 

12 

12 

12 

10 

10 

9 

9 

7 

7 

7 

6 

6 

•no^soa  ‘sir JO M ^nioa  AlO 

15 

13 

11 

10 

9 

8 

8 

8 

8 

7 

7 

5 

5 

5 

•uo:rsoa  ‘iCnBdnioo 
soiJV  poB  s:}n2q;  nBOiiaray 

14 

13 

13 

12 

11 

10 

9 

8 

8 

7 

•nuoo 

‘pjoj? JBH  ‘qoBag  ^ j^tupoo^i 

20 

18 

16 

14 

12 

12 

11 

10 

10 

8 

8 

7 

'7 

6 

6 

5 

5 

5 

•BJaq^oaa  qonqjB:rg 

11 

11 

10 

9 

8 

7 

7 

6 

6 

6 

5 

5 

5 

•no!} 

-soa  ^rsBg  ‘snpiv  ^ .^Cb^obh 

00 

16 

14 

12 

12 

11 

8 

8 

7 

7 

6 

6 

6 

6 

•sqjoA\.  ROJi  Ui^iqooja  ^!^nog 

16 

12 

11 

10 

9 

8 

8 

8 

8 

8 

8 

6 & 8 

8 

6&8 

•iCuBdraoo  oniqoBH  raa^Bg 

24 

20 

16 

14 

14 

12 

12 

10 

10 

8 

8 

7 

7 

7 

6 

6 

6 

5 

•qjOA 

Avail  ‘sqjOAi  ROJi  uoana 

o 

16 

13 

12 

11 

10 

9 

8 

8 

7 

6 

6 

6 

5 

5 

5 

•qjoA 

Avajq  ‘sqjoAV  Roji  JaA;a  q^JOKE 

00 

16 

13 



10 

10 

9 

8 

6 

6 

5 

•pa  ‘ao| 

-SntnipA\.‘'O0  ^ sanop  ‘jfasna 

20 

20 

16 

16 

12 

12 

11 

10 

9 

8 

7 

7 

6 

6 

5 

5 

5 

4 

•XuBdnioo  eaTqoBj\[  paAvoa 

20 

16 

16 

12 

12 

10 

10 

10 

10 

10 

9 

7 

7 

7 

7 

7 

6 

6 

•ajouii^IBa  ‘^RRH  ^ lOon 

20 

18 

16 

14 

12 

12 

11 

10 

9 

8 

7 

7 

7 

7 

6 

6 

6 

6 

•pa  ‘oo;3nini 

•TTAi'q^-iOAvsanTqoH  ^ RJapBH 

20 

18 

16 

14 

12 

12 

11 

10 

9 

8 

8 

8 

6 

6 

6 

6 

6 

6 

•qjOA 

Avail  ‘S^IJO^  UOJI  if^rpAOil 

oao«dcoci(yir-4005c»«o;ococo>rtidxdid 

•OQ  ani3na  raBa^g  aouapiAoja 

20 

20 

16 

16 

14 

14 

12 

10 

10 

10 

8 

8 

8 

8 

6 

6 

6 

6 

.So 

'O  A 


i4»nM’»+orH 


.d  .d  .4  .d  .d 


^d  a d ^d  ,g 


2 iucheB 


11 


12 


The  full  red  line  represents  Whitworth’s  S3^stem  of  pitches,  so 
modified  as  to  avoid  as  far  as  practicable  the  use  of  fractional  threads. 
The  law  of  the  system  would  be  represented  by  a fair  curve,  cutting 
this  broken  line  in  such  a manner  that  the  areas  included  between 
the  two,  above  and  below  the  former,  should  be  as  nearly  equal  as 
possible. 

The  straight  blue  line  represents  the  law  of  Mr.  iBriggs’s  system  of 
pitches,  the  peculiarity  of  which  consists  in  the  fact  that  the  pitches 
vary  nearly  with  the  diameters  of  the  bolts.  This  gives  excessively 
deep  threads  for  the  larger  bolts,  and  thus  seriously  diminishes  their 
effective  resisting  sectional  areas.  It  is  proper  to  remark  however, 
in  this  connection,  that  Mr.  Briggs  does  not  propose  to  extend  his 
system  beyond  bolts  of  two  inches  diameter,  up  to  which  point  the 
pitches  and  corresponding  depths  of  thread  do  not  materially  differ 
from  other  systems  or  the  general  practice  of  the  countr}". 

The  curve  in  black  represents  the  law  of  Mr.  Sellers’s  system,  the 
object  of  which  seems  to  have  been  to  effect  a sort  of  compromise 
between  the  various  practices  of  American  mechanics,  with  the  view 
of  uniting  them  upon  a uniform  system,  which  would  answer  all  the 
requirements  of  practice  and  at  the  same  time  relieve  them  from  the 
serious  inconvenience  inseparable  from  the  emploj^ment  of  different 
systems  by  different  manufacturers  of  machinery. 

Mr.  Sellers  has  constructed  the  following  empirical  formula, ^which 
determines  his  curves,  and  serves,  independently  of  tables  or  other 
aids,  to  determine  the  pitch  of  the  thread  of  any  required  bolt: 


in  which  d z=z  the  number  of  sixteenths  in  the  diameter  of  the  bolt, 
~|-  10  ; a 2.909  ] c = 16.64,  and  p = pitch  of  the  thread. 

A simpler  and  more  convenient  form  of  this  equation,  and  one 
wliich  is  readily  deduced  from  it  is: 

27  =:  0. 24  V D + 0. 625  — 0. 175 ; 
in  which  D represents  the  diameter  of  the  bolt  in  inches. 

To  illustrate  the  use  of  this  formula,  we  take  for  example,  a two-inch 
bolt,  and  let  it  be  required  to  determine  the  pitch  of  the  thread,  and 
the  number  of  threads  per  inch.  Making^  the  proper  substitution, 
the  formula  becomes — 

29=  0.24V  2 + 0.625  — 0.175 
= 0. 24  VX^— 0.175 
' = 0.24x1.62  — 0.175 

= 0.2138  of  an  inch,  , . ■ ■ ■ • ■ 


13 


The  reciprocal  of  this,  or  0:21  3 s = 4.68,  gives  the  proper  number 
of  threads  per  inch. 

For  the  purpose  of  avoiding  the  use  of  troublesome  fractions,  the 
nearest  convenient  aliquot  or  4|  is  taken.  This  will  be  found  to 
correspond  with  the  number  of  threads  given  in  the  table. 

In  this  slight  deviation  from  the  exact  number  given  by  the  for- 
mula we  have  the  explanation  of  the  broken  and  irregular  character' 
of  the  black  dotted  line,  which  represents  the  system  of  Mr.  Sellers, 
as  modified  to  mee^  the  practical  requirement  of  avoiding  the  neces- 
sity for  complicated  screw-cutting  gear,  by  preventing,  as  far  as  prac- 
'ticable,  the  use  of  fractional  threads. 

The  blue  dotted  line  representing  the  practice  of  the  Baldwin 
Locomotive  Works  of  this  city,  although  showing  that  a much  finer 
pitch  is  used  for  nearly  all  bolts  than  is  given  by  either  Whitworth’s 
or  Sellers’s  systems,  shows  nevertheless,  that  the  practice  of  this 
establishment  is  entirely  without  system. 

It  is  claimed  that  for  locomotive  and  other  special  purposes,  finer 
pitches  are  required  in  order  to  prevent  the  nuts  from  jarring  loose 
and  working  off. 

When  it  is  remembered,  however,  that  the  influence  of  pitch  upon 
the’ tendency  of  the  nut  to  turn  upon  the  bolt  is  very  slight,  in  com- 
parison with  the  effect  of  friction  between  the  thread  surfaces  and 
upon  the  base  of  the  nut,  it  would  seem  that  the  necessity  for  exces- 
sively fine  pitches  is  more  imaginary  than  real.  Indeed  an  examina- 
tion of  the  practice  of  these  works  shows  that  the  |-inch  bolt,  which 
from  its  size  is  we  presume  used  as  extensively  upon  locomotives  as 
any  other,  has  the  same  pitch  as  is  recommended  for  the  same  sized 
bolt  by  both  Whitworth  and  Sellers. 

We  feel  authorized,  therefore,  in  assuming  that  either  Whitworth’s 
or  Sellers’s  systems  of  pitches  would  answer  the  purpose  of  the  loco- 
motive builders  quite  as  well  as  the  slightly  finer  pitches  now  used  ; 
especially  is  this  the  case  when  the  advantages  to  be  derived  from 
uniformity  of  practice  are  considered. 

The  deviation  of  the  practice  of  Messrs.  Pusey,  Jones  & Co.,  from 
the  average  practice  and  in  the  direction  of  coarse  pitches  is  equally 
marked,  and  shows  equally  a want  of  system.  The  entire  practice 
of  the  engineers  of  our  country  would  probably  be  found  between 
these  two  extreme  limits,  and  the  average,  if  we  could  obtain  it,  we 
feel  assured  would  not  materially  differ  from  the  systems  of  Whit- 
worth or  Sellers. 

In  fixing  upon  a standard  system  regard  should  be  had  to  the 
practice  of  the  greater  number  of  engineers,  unless  there  be  some- 


14 


thing  radically  wrong  in  that  practice.  As  the  only  serious  defect  we 
are  able  to  discover  is  want  of  system,  and  as  the  average  practice 
may  be  represented  by  either  Whitworth^ s or  Sellers’s  systems,  we 
have  only  to  select  one  of  these  as  a standard. 

Considering  these  two  systems  we  find  no  material  difference  exist- 
ing between  them.  In  their  general  characteristics  they  differ  in 
that,  up  to  bolts  of  two  inches  diameter,  the  pitches  of  the  Whitworth 
system  are  coarser  and  the  bolts  weaker  than  in  the  Sellers  system. 
Above  two  inches  the  reverse  occurs  ; the  pitches  of  the  Whitworth 
system  becoming  slightly  finer  and  the  bolts  slightly  stronger  than  in 
that  proposed  by  Mr.  Sellers.  The  most  marked  difference,  however, 
exists  in  the  case  of  the  J-inch  bolt,  which,  in  the  Whitworth  system, 
has  12,  and  in  the  Sellers  system  13  threads  per  inch.  The  strength 
of  this  bolt  is  therefore  much  greater,  and  its  liability  to  twist  off 
very  much  diminished  in  the  Sellers  system. 

Again,  Mr.  Sellers’s  system  is  one  which,  by  the  use  of  the  formula, 
or  equation  of  the  curve  representing  its  law,  admits  of  indefinite 
extension.  Moreover,  by  far  the  greater  number  of  establishments 
which  we  have  visited  or  with  which  we  have  communicated  have 
either  already  adopted,  intend,  or  are  willing  to  adopt  it. 

The  board  therefore  recommends  the  adoption  of  Mr.  Sellers’s 
system  of  pitches  as  the  standard  for  the  navy. 

II. — Form  op  thread. 

For  the  general  purposes  of  bolts  and  nuts,  there  are  four  difterent 
forms  of  thread  now  in  use.  These  are  the  ordinary  sharp  Y,  the 
Whitworth,  the  Briggs,  and  the  Sellers  forms. 

The  sharp  Y thread.  Fig.  1,  Plate  II,  has  its  surfaces  inclined  to 
each  other  at  an  angle  of  60°.  A section  of  this  thread  is  therefore 
an  equilateral  triangle,  each  side  of  which  is  equal  to  the  pitch  of 
the  screw,  and  the  depth  of  the  thread,  measured  perpendicularly  to 
the  axis  of  the  bolt,  will  be  expressed  by  the  formula. 

d z=zpcos  30° 

= . 866  p, 

in  which  p z=  represents  the  pitch,  d the  depth  of  the  thread,  and  30° 
half  the  angle  included  between  the  thread  surfaces. 

The  effective  diameter  of  the  bolt  is  expressed  by  the  formula 
c?  = D — 2 X .866^. 

= D — 1.732  p. 

in  which  D and  d represent  the  nominal  and  effective  diameters 
respectively. 


Fi;)  I.  'f  Thmu! ) 


Pill.-  II 


I'uf.  ? iSrIlcrs  TUiriid ! 


15 


The  Whitworth  thread,  Fig.  3,  has  its  plane  sides  inclined  to  each 
other  at  an  angle  of  55°,  with  the  angle  formed  by  these  surfaces,  at 
both  the  periphery  and  root  of  the  thread,  so  rounded  that  the  depth 
of  the  finished  thread  is  two-thirds  the  depth  of  a Y thread,  having 
its  surfaces  inclined  at  an  angle  of  55°.  This  form  is  represented 
more  in  detail  in  Fig.  4,  where  the  depth  of  a Y thread  is  divided 
by  lines  parallel  to  the  axis  of  the  bolt  into  six  equal  parts,  and  the 
curved  form  secured  by  inscribing  arcs  of  circles  within  the  straight 
sides  of  the  thread  and  the  extreme  dividing  lines. 

In  this  form  of  thread  the  depth  is  determined  by  the  formula 

d ■“  % V P 

2.  tan  27°  30' 

= .65  p, 

and  the  diameter  of  the  effective  section  of  the  bolt  by 

cZ  = D — 2 X .65 
= D — 1.3 

The  form  of  thread  proposed  by  Mr.  Briggs  resembles  that  of  the 
Whitworth  thread,  but  differs  from  it,  in  that  the  thread  surfaces  are 
inclined  at  an  angle  of  60°,  and  in  that  the  angles  of  the  thread  are 
rounded  just  enough  to  reduce  the  depth  of  the  thread  to  0.8  “for 
best  workshop  bolts, or  to  0.75  jp  “for. good  merchantable  bolts 
With  this  form,  therefore,  the  effective  diameters  of  the  two  classes 
of  bolts  would  be 

cZznD  — 2 X .8^. 

=:D  — 1.6^, 

and 

cZ  = D — 2 X .75  p. 
z=  D — 1.5  p, 

respectively. 

Mr.  Sellers  proposes  the  form  of  thread  represented  in  Fig.  2.  It 
is  simply  the  ordinary  Y thread  with  surfaces  inclined  at  an  angle  of 
60°,  and  with  the  angles  cut  off  at  the  top  and  filled  in  at  the 
bottom  to  the  extent  of  one-eighth  of  the  depth  of  the  Y thread  each, 
so  that  the  depth  of  the  thread  is  three-fourths  that  of  the  ordinary 
Y form,  and  is  expressed  by  the  formula 

^ = I ^ cos  30°. 

==  .65  p. 

The  effective  diameter  will  then  be 

cZ  = D — 2 X .65  jp. 
z=  D — 1.30  jp. 


16 


Collecting  our  results  for  the  effective  diameters  of  bolts  having 
threads  of  the  different  forms,  we  have 

form,  c?  = D — 1.732  p. 

Whitworth  “ c?  = D — 1.3^. 

Brig-ffs  “ 1.6  jp. 

Briggs  ]c^  = D — 1.5p. 

Sellers  “ dzzzJ)  — 1.3  p. 

With  equal  pitches  it  appears,  therefore,  that  the  maximum  effect- 
ive diameter  of  bolt  is  insured  when  threads  of  the  Whitworth  or 
Sellers  forms  are  used,  while  the  usual  Y form  insures  the  minimum 
effective  diameter. 

The  ability  of  a bolt  to  resist  tensile  strain  varies  as  the  square, 
while  its  ability  to  resist  torsional  strains  varies  as  the  cube  of  its 
effective  diameter. 

In  order  to  show  more  clearly  the  relative  merits  of  the  different 
forms  of  thread  under  consideration,  we  have  constructed  the  follow- 
ing table  (II). 


Table  II. — Showing  the  tensional  and  torsional  strengths  of  holts  having  the 
Sellers  thread f as  compared  with  holts  having  the  common  sharp  V thread. 


Nominal  diameter  of  bolt. 

d\ 

d,\ 

d,^ 

d?' 

i inch 

.02666 

. 03422 

. 004355 

. 006331 

1.  283 

1.  454 

5-16  inch 

. 04879 

. 05760 

. 010120 

.01382 

1.  231 

1. 366 

f inch 

. 07113 

. 08644 

. 018970 

. 02541 

1.215 

1.  339 

7-16  inch 

. 09847 

.11902 

. 030899 

. 041064 

1.209 

1. 329 

i inch 

. 13452 

. 16000 

. 04935 

. 06400 

1. 189 

1.297 

9-16  inch .* 

. 17488 

. 20612 

. 073139 

. 09358 

1.178 

1.  280 

i inch 

. 21855 

. 25703 

. 10217 

. 13032 

1. 176 

1.  275 

J inch 

. 33260 

. 38440 

. 19191 

. 23833 

1. 155 

1.242 

1 inch 

. 46649 

. 53435 

. 31861 

. 39063 

1.146 

1. 223 

1 inch 

. 61387 

. 70060 

. 48098 

. 57305 

1.141 

1. 219 

li  inch 

. 77087 

. 88360 

. 67682 

. 83060 

1. 146 

1.227 

li  inch  

1.  0060 

1. 1342 

1.  0090 

1.  2080 

1. 127 

1. 197 

If  inch 

1. 1794 

1. 3455 

1.  2807 

1.  5«05 

1. 141 

1. 218 

If  inch 

1. 4664 

1.  6486 

1.  7758 

2. 1170 

1. 124 

1. 192 

If  inch 

1.  7161 

1.  9293 

2.  2481 

2.  6798 

1. 124 

. 1. 192 

If  inch  

1.  9712 

2.  2231 

2.  7677 

3.  3150 

1. 128 

1.198 

If  inch 

2.  3379 

2.  6114 

3.  5747 

4.  2201 

1.117 

1. 181 

2 inches 

2.  6082 

2.  9305 

4.  2122 

5.  0177 

1. 124 

1. 191 

2f inches 

3. 4782 

3.  8495 

6.  4870 

7.  5527 

1. 107 

1. 164 

2i  inches 

4.  2725 

4.  7350 

8.  8312 

10.  303 

1. 108 

1. 167 

2f  inches - 

5.  3686 

5.  8854 

12.  438 

14.  274 

1.096 

1.148 

3 inches 

6.  2750 

6.  9103 

15.  719 

18. 171 

1.101 

1. 156 

inches 

7.  5900 

8. 2885 

20.  911 

23.  863 

1.092 

1. 141 

3f  inches 

8.  8032 

9.  6100 

26. 119 

29,  791 

1.  092 

1. 143 

3f  inches 

10.  068 

11.  003 

31. 946 

36.  497 

1.093 

1. 142 

4 inches , 

11.716 

12.  723 

40. 108 

45.  384 

1.086 

1. 131 

4f  inches 

13.  307 

14. 427 

48.  546 

54,  784 

1.  084* 

1.119 

4f inches 

14,  996 

16.  602 

57.  960 

65.  353 

1.083 

1. 127 

4f  inches 

16.  726 

18. 113 

68.417 

77.  090 

1.083 

1. 127 

5 inches 

18.  550 

20.  070 

79.  894 

89.  916 

1.082 

1. 125 

inches 

20.  766 

22.  372 

94.  632 

105.  820 

1.  077 

1.118 

si  inches 

22.  762 

24.  532 

108.  60 

121.  510 

1.078 

1,119 

5f  inches 

25.  21 0 

27.  070 

126.  57 

140.840 

1.  074 

1.113 

6 inches 

27.  353 

29.  403 

143.  05 

159,  470 

1.075 

1.115 

The  first  column  contains  the  nominal  diameters  of  the  bolts;  d=. 
effective  diameter  of  bolt  having  the  common  Y-thread;  and  the 


17 


effective  diameter  of  bolt  liaving  threads  of  the  Sellers  or  Whitworth 


forms;  ^ expresses  the  ability  to  resist  tensile  strain  of  a bolt  having 

threads  of  the  Sellers  or  Whitworth  forms,  as  compared  with  that  of 

d ^ 

the  same  bolt  having  a thread  of  the  ordinary  V form.  expresses 


the  ability  to  resist  torsional  strain  of  a bolt  having  threads  of  the 
Whitworth  or  Sellers  forms,  as  compared  with  that  of  the  same  bolt 
having  a thread  of  the  ordinary  Y form. 

From  the  table  it  appears  that  in  the  |-inch  bolt  the  Sellers  or 
Whitworth  form  of  thread  insure  28  per  cent,  more  tensile  strength 
than  the  sharp  Y thread;  while  in  the  extreme  case  of  a G-inch  bolt 
the  tensile  strength  is  still  seven  per  cent,  greater.  The  effect  upon 
the  ability  of  the  bolt  to  resist  torsional  strain  is  still  more  marked  ; 
the  I -inch  and  6 -inch  bolts  being  respectively  45  and  11  per  cent, 
stronger  with  the  Sellers  or  Yfhitwortli  than  with  the  common  Y 
thread. 

In  the  more  frequent  case  of  the  inch  bolt,  the  tensile  and  torsional 
strengths  are,  respectively,  14  and  22  per  cent,  greater  with  Whit- 
worth’s or  Sellers’s  threads  than  with  the  Y thread. 

The  Briggs  form  possesses  an  advantage  of  the  same  kind,  but 
much  less  in  extent. 

An  additional  and  very  serious  element  of  weakness  in  the  Y form 
is  the  sharp  angle  at  the  root  of  the  thread.  The  precise  amount  of 
the  weakening  effect  due  to  this  cause  cannot,  in  the  present  state  of 
our  knowledge,  be  stated  ; it  is  nevertheless  known  to  be  very  con- 
siderable— probably  not  less  than  20  or  25  per  cent.  This  element 
of  weakness  is  practically  eliminated  in  all  the  other  forms  of  threads. 

In  order  to  show  more  clearly  the  importance  of  preserving  the 
torsional  strength  of  bolts,  or  of  limiting  the  depth  of  the  screw- 
thread  to  the  smallest  practicable  amount,  we  have  instituted  the 
following  comparison  of  tensional  and  torsional  strains  upon  bolts: 

The  torsional  or  twisting  strain  upon  a bolt,  due  to  screwing  up  the 
nut,  has  its  application  upon  the  thread  of  the  screw,  and  results  from 
the  friction  between  the  thread  surfiices,  together  with  that  compo- 
nent of  the  load  which  has  to  be  overcome  in  order  to  move  it  up  the 
inclined  plane  formed  by  the  screw  surface.  It  follows,  therefore, 
that  in  bolts  of  different  sizes,  this  twisting  force  will  have  its  point 
of  application  at  distances  from  the  axis  varying  directly  as  the 
radius  or  diameter  of  the  bolt,  and  the  measure  of  its  effect  will  be 
the  product  of  the  force  exerted,  multiplied  by  the  arm  or  the  dis- 
tance between  its  point  of  application  and  the  axis  of  the  bolt. 

2 


18 


If  then  we  put 

T — the  measure  of  the  resistance  of  the  bolt  to  torsion; 
d diameter  of  the  bolt, 
we  shall  have 

r oc  d\ 

But  the  force  to  be  exerted  in  order  to  produce  the  effect  r,  or  to 
twist  the  bolt  asunder,  varies  directly  as  r,  and  inversely  as  its  lever 
arm;  and,  as  before  stated,  this  lever  arm  varies  directly  as  the 
diameter  of  the  bolt.  Hence,  if  we  put  F = the  force  applied  upon 
the  screw-thread,  we -have 


F oc 


oc 


oc 


Whence  follows  that  the  force  which  may  be  safely  applied  to  the 
surface  of  a screw-thread  for  the  purpose  of  turning  the  bolt,  or 
which  may  be  transmitted  to  it  through  the  medium  of  the  nut,  varies 
as  the  square  of  the  diameter  of  the  bolt,  or  in  accordance  with  the 
same  law  that  governs  the  tensile  strains  which  may  be  placed  upon 
bolts  or  other  cylindrical  rods. 

If  the  inclination  of  the  screw-thread  be  constant  for  all  bolts,  and 
the  coefficient  of  friction  between  the  thread  surfaces  be  uniform,  the 
force  F will  always  be  the  same  function  of  the  load  or  strain  upon 
the  bolt;  in  other  words,  there  will  always  be  the  same  relation 
between  the  tendencies  to  break  the  bolt  longitudinally  and  to  tAvist 
it  off. 

In  the  case  of  the  system  of  pitches  recommended,  however,  the 
inclination  of  the  screw-thread  is  not  constant,  it  being  greater  upon 
small  bolts,  and  gradually  diminishing  as  the  bolts  become  larger. 

The  force  F required  to  strain  a large  bolt  up  to  any  desired  limit, 
neglecting  friction,  varies  Avith  the  tangent  of  the  angle  of  inclination 
of  the  thread;  and  since  the  effect  of  friction  will  be  the  same  Avhat- 
ever  be  the  pitch  or  angle  of  inclination,  it  will  folloAv  that  the  largest 
value  of  F (relatively)  would  be  required,  and  the  greatest  tendency 
to  tAvist  off  would  therefore  exist  in  the  smallest  bolt  ; yet  the  abso- 
lute difference  between  the  inclinations  of  the  threads  of  the  smallest 
and  largest  bolt  is  so  slight,  and  as 'the  effort  required  to  overcome 
the  effect  of  inclination  of  the  thread  is  so  very  small,  Avhen  compared 
AAuth  that  required  to  overcome  the  friction,  that  Ave  might,  without 
appreciable  or  considerable  error,  regard  it  as  constant. 

We  Avill,  hoAvever,  take  the  most  unfavorable  case — that  of  the 
J-inch  bolt,  the  smallest  of  the  proposed  system — Avhcre  the  inclination 


19 


of  the  thread  is  at  its  maximum,  and  consequently  where  the  tendency 
to  twist  the  bolt  asunder  is  also  at  its  maximum. 

Let  W = load  or  strain  upon  the  bolt. 

d — inclination  of  an  element  of  the  thread  surface  lying  midway 
between  its  root  and  periphery. 

p z=z  angle  of  friction. 

F = force  applied  upon  the  element  of  the  thread  surface  whose 
inclination  is  0. 

Then 

F 1=  W tan  (d  + p>) 

The  value  of  p is  determined  by  the  coefficient  of  friction,  which 
is  equal  to  tan  p. 

Taking  the  coefficient  of  friction  — tan  p — 0.124,  we  have 


Again 


p =:  70  04'; 


circ. 


Nov/  for  the  |-inch  bolt,  having  20  threads  per  inch,  the  pitch  will 
be  .05  of  an  inch,  and  the  diameter  of  the  circle  lying  midway 

between  the  root  and  periphery  of  the  thread  will  be 


X 3.1416  .2175X3.1416  0.6833 


tan  u — 


,05 


r=.0732 


and 

Hence 


0.6833 
dz=z4:^  11'. 

d + p = 4:^  IV  + 7°  04'. 
= 11°  15'. 


F — W tan  (d  + p.) 

=z  W tan  IP  15'. 
rz:0.2W. 

The  ultimate  tensile  strength  of  a J-inch  wrought-iron  bolt,  with 
20  threads  per  inch  of  the  Sellers  form,  and  consequently  having  an 
effective  diameter  of  0.185  of  an  inch,  will  be  about 
W — .7854x0.H85x60000 
= 1612. 8 pounds  : 

whence 

F =:  0.2x1612.8 
= 322.56  pounds. 

It  appears,  therefore,  that  a force  of  322.56  pounds  must  bo  exerted 
upon  the  thread,  in  a direction  tangent  to  the  circumference  of  the 
bolt,  and  perpendicular  to  its  axis,  in  order  to  break  the  bolt  longi- 
tudinally. 

Let  us  next  see  how  great  a force  F'  must  be  applied  at  the  same 


20 


point,  and  in  the  same  direction,  in  order  to  twist  the  bolt  off.  For 
this  purpose  500  pounds  may  be  taken  as  the  force  which  is  required 
to  twist  off  an  iron  rod  one  inch  in  diameter;  the  force  being  applied 
at  a distance  of  12  inches  from  the  axis  of  the  rod. 

Then,  since  the  force  to  be  applied  varies  directly  as  the  cube  of 
the  diameters  of  the  rod,  and  inversely  as  the  lever  arm  with  which 
it  acts,  we  have 

500x0.^85x24 


F'; 


.2175 


348  pounds,  nearly. 


It  appears,  therefore,  that  under  the  conditions  assumed,  the  bolt 
having  the  form  of  thread  which  insures  greatest  strength,  and  the 
surfaces  of  the  threads  being  clean  and  well  lubricated,  the  tenden- 
cies to  yield  to  the  tensile  and  torsional  strains  are  about  equal. 

Practically,  however,  the  threads  of  screws  are  often  in  a more 
unfavorable  condition  than  that  assumed,  owing  to  accumulation  of 
dirt,  abrasion  of  the  surfaces  and  increased  viscidity  of  the  lubricant, 
all  of  which  increase  the  friction,  and  consequently  the  tendency  of 
the  bolt  to  yield  to  torsional  strain. 

In  view  of  these  considerations  the  necessity  of  selecting  that  form 
of  thread  which  insures  the  maximum  strength  of  bolt,  seems  to  be 
imperative. 

As  a matter  of  peculiar  interest  in  this  connection,  let  us  next 
ascertain  how  much  the  friction  between  the  thread  surfaces  may  be 
increased  by  the  causes  just  mentioned,  before  the  bolt  will  yield  to 
the  torsional  strain  required  to  strain  it  up  to  one-third  its  ultimate 
tensile  strength — a limit  which  should  of  course  never  be  exceeded 
in  practice. 

To  satisfy  this  condition  we  have 

348  = Jx  1612.8  tan((9  + ^); 

whence 

tan  + = 0.647, 


and 

But 


{d  + p)=i  32°  54'. 

<9  = 4°  11' 

/.  P =:  32°  54'— 4°  IP 
= 28°  43', 


and  tan./>=.548 

— increased  coefficient  of  friction. 


Comparing  this  result  with  the  coefficient  of  friction  between  clean 
and  well-lubricated  surfaces,  we  find  that  the  friction  may  be  in- 
creased = times,  nearly,  before  the  bolt  will  be  twisted  off, 


1' 


21 


while  straining  it  up  to  its  safe  limit  of  tensile  strength,  by  screwing 
up  the  nut. 

The  Whitworth  and  Sellers  forms  of  thread  satisfying  the  require- 
ment of  strength  equally  well,  it  remains  to  examine  them  in  reference 
to  their  relative  abilities  to  satisfy  other  conditions,  such  as  suitable 
bearing  surface  and  ease  of  perfect  execution. 

The  bearing  surface  of  the  Whitworth  thread  is  practically  limited 
to  the  straight  portion  of  the  surface;  while  in  the  Sellers  thread, 
the  entire  surface  between  the  flat  at  the  top  and  bottom  may  be 
regarded  as  effective  bearing  surface.  In  this  particular,  therefore, 
the  preference  must  be  awarded  to  the  Sellers  thread. 

In  regard  to  the  execution  of  the  Whitworth  form  of  thread,  we 
remark  that  its  angle  is  such  as  not  to  admit  of  ready  verification,  and 
its  curved  top  and  bottom  require  such  a multiplicity  of  special  tools, 
and  such  skill  on  the  part  of  the  workman,  that  the  requisite  degree 
of  uniformity  of  practice,  auiorg  different  manufacturers,  is  believed 
to  be  entirely  impracticable,  if  not  impossible. 

xkraong  all  the  establishments  visited  or  communicated  with  by  us, 
onl}^  one  has  been  found  where  this  form  of  thread  is  used.  We  refer 
to  the  printing  press  manufactory  of  Messrs.  R.  Hoe  & Co.,  of  New 
York  city,  where  the  thread  has  been  in  use  for  about  thirty  years. 
The  fact  that  this  thread,  in  itself  undoubtedly  the  best  form  ever 
proposed,  has  been  so  long  before  the  public,  and  has  met  with  so 
little  favor  from  our  engineers,  is  of  itself  the  strongest  and  the  most 
conclusive  argument  that  can  be  urged  against  its  practicability. 

The  angle  of  the  Sellers  thread  being  60^,  admits  of  easy  construc- 
tion and  ready  verification.  The  cutting  tool  used  in  the  production 
of  this  thread  is  precisely  like  that  employed  in  cutting  the  common 
y thread,  except  that  its  point  is  flattened  by  a certain  definite 
amount,  which  is  determined  by  accurate  steel  gauges,  now  being 
manufactured  by  Messrs.  Brown  & Sharpe,  of  Providence,  R.  I. 

It  has  been  urged  by  some  that  the  Sellers  thread  will  degenerate 
into  the  Whitworth  form.  That  the  Sellers  thread  degenerates  there 
can  be  no  doubt,  but  the  same  objection  applies  with  equal  or  greater 
force  to  the  other  forms.  The  board  is,  however,  unable  to  discover 
that  such  degeneration  would  be  attended  by  any  more  serious  incon- 
venience than  would  result  from  the  deterioration  of  the  other  forms. 
It  is  of  the  opinion  that  the  amount  and  effect  of  wear  upon  the  thread 
and  upon  the  taps  and  dies  with  which  it  is  cut,  would  be  less  serious 
in  the  case  of  the  Sellers  than  in  the  case  of  either  of  the  other 
forms  proposed.  An  exception  may  possibly  exist  in  the  case  of  the 
Whitworth  form,  which  cannot  however  be  recommended,  on  account 


22 


of  the  difficulties  with  which  its  accurate  production,  in  the  first 
instance,  is  attended. 

All  the  advantages  of  the  Whitworth  over  the  ordinary  V thread, 
as  regards  strength  and  liability  of  the  edge  of  the  thread  to  injury, 
with  the  additional  and  very  important  advantage  of  ease  of  produc- 
tion, being  possessed  by  the  Sellers  thread,  and  in  view  of  the  marked 
favor  accorded  it  by  engineers  generally,  the  board  unhesitatingly 
recommends  it  as  a standard  for  the  navy. 

III. — Dimensions  of  the  nut. 

Nuts  may  yield  either  by  the  stripping  of  the  threads  or  by  burst- 
ing. In  order  that  the  thread  may  not  strip,  the  depth  of  the  nut 
must  be  such  as  to  offer  a resistance  to  shearing  strain,  at  the  root  of 
the  thread,  equal  to  the  resistance  of  the  effective  section  of  the  bolt 
to  tensile  strain. 

The  resistance  to  shearing  strains  in  iron  being  only  0.8  the  resist- 
ance to  tensile  strain,  it  follows  that  the  cylindrical  surface,  formed 
by  the  junction  of  the  root  of  the  thread  with  the  body  of  the  bolt, 
should  be  to  the  effective  transverse  section  of  the  bolt  in  the  ratio 
of  1 to  0.8.  Again,  owing  to  the  flattening  of  the  thread  at  top  and 
bottom,  only  of  the  pitch  is  effective  to  resist  shearing  strain. 
Hence,  putting  H zz:  the  requisite  depth  of  nut  to  meet  the  require- 
ment under  consideration,  we  have  the  following  relation: 

.25  TT  0.8X0. 875  ;r  d H. 
whence  .25  c?zz:  0.7000  H; 

and  H=^cl 

= 0.357(1 

Hence  for  new  and  perfect  fitting  threads,  0.357  of  the  effective 
diameter  of  the  bolt  would  meet  the  requirement  of  strength  to  resist 
stripping  of  the  thread.  But  when,  in  consequence  of  wear,  the 
fitting  of  the  thread  surfaces  ceases  to  be  perfect,  the  strain  upon  the 
thread  is  no  longer  a shearing  strain,  and  the  thread  acts  in  the 
capacity  of  a beam  fixed  at  one  end  and  loaded  at  a little  distance  out. 

In  that  case  a greater  depth  of  nut  is  required.  Probably  a depth 
of  nut  equal  to  half  the  nominal  diameter  of  the  bolt  would,  in  all 
cases,  be  ample  to  meet  the  requirement  of  strength  alone. 

Again,  the  depth  of  the  nut  should  be  such  as  to  afford  a good  hold 
for  the  wrench,  and,  what  is  still  more  important,  should  be  such  as 
to  afford  an  extent  of  bearing  surface  upon  the  thread  which  will 
effectually  prevent  undue  abrasion  of  its  surface. 

It  is  difficult  to  decide  upon  the  pressure  per  square  inch  to  which  . 


23 


the  surface  of  a screw  thread  may  be  safely  subjected.  However, 
as  nuts  having  depths  equal  to  the  nominal  diameters  of  their  bolts 
are  found  to  work  well  in  practice,  a determination  of  the  pressure 
habitually  borne  by  their  thread  surfaces  may  throw  some  light  upon 
this  point. 

The  following  table  (III)  shows  the  effective  areas  of  bolts  of  the 
different  sizes,  the  projected  areas  of  their  thread  surfaces,  within  a 
distance  equal  to  their  nominal  diameters,  and  the  ratio  of  the  two  : 


Table  III. — Showing  the  ratio  of  the  pressure  per  square  inch  upon  thread 
surface^  to  the  tensile  strain  per  square  inch  upon  the  effective  section  of  the 
holt,  ( Sellers  thread.) 


Nominal  diameter  of 
bolt. — D. 

W 

a II 

1* 

w 

Projected  bear- 
ing aurface  of 
thread— 

s 

~s‘ 

Nominal  diameter  of 
bolt.— D. 

i =«• 

sji 

(15  — 

Projected  bear- 

ing surface  of 
thread — S. 

s 

's' 

-j-  inf'll  . - . 

. 02688 

. 11105 

.242 

2 inches 

2.  3019 

7.  5573 

.3046 

5-16  inch 

. 04524 

. 17696 

.2556 

2i  inches 

3. 02.32 

9.  6471 

. 3134 

J inch 

. 06789 

. 25536 

.266 

2^  inches 

3. 7188 

11.  8990 

.3125 

7-1 6 inch 

. 09347 

. 34826 

.2684 

2%  inches 

4.  6224 

14. 4881 

.3190 

•.1  inch 

. 12566 

. 45949 

.273 

3 inches 

5. 4283 

17. 2221 

.3150 

9-16  inch 

.16189 

.58461 

.2769 

3i  inches 

6.  5009 

20.  4158 

. 3188 

^ inch 

. 20174 

. 72222 

.2795 

3^ inches  

7.  5477 

23.  5849 

. 3200 

j-  inch  

. 30190 

1.  0470 

.288 

3J inches  

8.  6416 

27.  0337 

. 3196 

i inch 

. 41969 

1.4303 

.293 

4 inches 

9.  9929 

30.  8820 

.3235 

1 inch 

. 55024 

1.8813 

.3112 

4^-  inches 

11. 328 

34,  9236 

.3244 

l-g-  inch 

. 69399 

2.  2877 

. 3033 

4i  inches 

12.  743 

40.  3586 

.3157 

ir  inch 

. 89082 

2. 94245 

.3027 

4J  inches 

14.  250 

43.  2728 

.3288 

inch 

1.  0568 

3.  5310 

.2993 

5 inches  

15.  763 

48.  4000 

. 3260 

inch 

1. 2948 

4.  2507 

.3051 

5i  inches 

17.  572 

53.  4950 

.3290 

li  inch 

].  5152 

4. 9925 

. 3035 

5i-  inches 

19.  267 

58.  6676 

.3280 

inch 

1.  7460 

5.  7750 

.3023 

5^  inches 

21.  262 

62.  7850 

.3286 

1 j inch 

2.  0510 

6.  6572 

.3081 

6 inches 

23.  098 

69.  8540 

.3310 

The  projected  area  of  thread  surface  is  found  as  follows: 

Let  D nominal  diameter  of  the  bolt  the  depth  of  the  nut. 
d — effective  diameter  of  the  bolt. 
n = number  of  threads  per  inch. 

Then  the  projected  surface 

S = 5 TT  (D^  — d")  X D 71. 

It  will  be  observed  that  as  the  bolts  increase  in  size,  the  pressure 
per  square  inch  upon  their  thread  surface  increases — varying  between 
0.'24  of  the  tensile  strain  for  the  |-inch,  and  0.33  for  the  6-inch  bolt. 
These  pressures  seem  excessive;  but  we  find  upon  examination  that 
the  under  surfaces  of  nuts  are  uniformly  subjected  to  pressures  quite 
equal  to  these. 

For  example,  let  us  take  the  case  of  a 2-inch  bolt  and  its  nut. 
Taking  the  largest  proportions  used,  the  short  diameter  of  such  a nut 
would  be  four  inches;  while  its  effective  bearing  surface — the  area  of 
the  circle  inscribed  within  its  base,  less  the  section  of  the  bolt — would 
be  12.5GG  — 3.142  = 9.424  square  inches. 


24 


The  effective  section  of  the  bolt  (with  V thread)  would  be  2.053 
square  inches. 


Hence  the  ratio 


2.053 

9.424 


— .207  shows  that  with  the  largest  proper 


tions  of  nut,  Avitli  the  deepest  thread,  and  with  the  weakest  bolt,  the 
pressure,  per  square  inch,  on  the  base  of  the  nut  is  0.207  of  the  ten- 
sile strain  per  square  inch  upon  the  bolt. 

Again,  taking  the  same  bolt,  and  the  smaller  but  more  usual  pro- 
portion of  nut,  where  the  long  diameter  is  made  twice  the  nominal 
diameter  of  the  bolt,  the  ratio  of  the  two  areas  is  0.276. 

It  appearing,  therefore,  that  the  rubbing  surfaces  of  nuts  are 
habitually  subjected  to  pressures  nearly  equal  to  and  in  some  instances 
greater  than  those  which  would  result  from  the  proposed  form  of 
thread,  with  depth  of  nut  equal  to  nominal  diameter  of  bolt,  we  are 
•of  the  opinion  that  for  permanent  bolts,  where  the  nut  is  rarely  dis- 
turbed, the  depth  of  the  nut  should  be  at  least  equal  to  the  nominal 
diameter  of  the  bolt.  For  special  cases,  where  the  nut  is  constantly 
being  turned,  its  depth  should  invariably  be  made  greater,  in  order 
to  prevent  a too  rapid  destruction  of  the  thread  surface. 

The  next,  and  only  remaining  point  to  be  considered,  in' connection 
with  the  nut,  is  its  tendency  to  burst. 

In  Fig.  5,  let 

T = load  on  bolt. 

p = normal  pressure  upon  one  half  the  thread,  resolved  in  a direc- 
tion perpendicular  to  any  single  element  of  its  lielicoidal  surface. 

B = component  of  P acting  in  a direction  perpendicularAo  the  axis 
of  the  bolt. 

<p  = half  the  angle  of  the  thread.  = 30^. 

Then 


whence 


zn  2 P cos 


2 cos  (f. 


But 


B =z  P sin 


r sin  ip, 
2 cos  if 


2 


tan  iP. 


Introducing  the  effect  of  friction,  which  diminishes  the  tendency 
of  the  force  B to  burst  the  nut,  the  preceding  becomes 

B=pan  — 


25 


Now  (p  — 30°  and  [)  lias  been  found  to  be  at  least  7°  04'.  Hence 
9-  — /:)=r30°— 7°  04'=i22°  56',  and 

B=:Uan  22°  56' 

A 

= |-X0.423 
= 0.2115  r 

It  follows,  therefore,  that  the  requisite  section  of  metal  in  the  niif 
to  prevent  bursting'  will  be  to  the  effective  section  of  the  bolt  as 
0.2115  to  1. 

Putting  A =:  short  diameter  of  nut. 
h z=:  depth  “ “ 

and  D diameter  of  bolt,  as  heretofore,  we  have 

A (A  — D)  = 0.2115x0.7854  Dh 
But  we  have  already  decided  that  7i  = D 
/,  D(A  — D)  = 0.166 

or  A — D=0.166D, 

whence  A = 1.166  D, 

from  which  it  appears  that,  neglecting  the  resistance  of  the  thread? 
and  taking  the  entire  section  of  the  bolt  as  effective,  the  short-diam- 
eter of  the  nut  need  be  only  one-sixth  greater  than  the  nominal 
diameter  of  the  bolt  to  effectually  prevent  bursting. 

A nut  with  these  proportions  would  have  neither  sufficient  bearing 
surface  upon  its  base,  nor  sufficient  strength  to  resist  tapping  strains. 

The  only  guide  we  have  in  providing  for  these  last  requirements  is 
to  be  found  in  the  general  practice  of  engineers.  In  the  course  of 
our  investigations  we  have  found  four  different  arbitrary  rules  for 
determining  the  diameter  of  nut,  which  are  as  follows : 

1st.  Long  diameter  of  nut  = twice  diameter  of  bolt. 

2d.  Short  “ “ “ = “ “ “ “ 

3d.  “ “ “ “ = 1.6  “ “ “ 

4th.  “ “ “ “ zz:  1.5  “ “ “ -f-  I". 

The  latter  of  these,  being  the  smallest,  having  borne  successfully 
the  test  of  practice,  and  being  a part  of  the  system  already  recom- 
mended, the  board  feels  constrained  to  recommend  it  as  a part  of  the 
standard  system  for  the  navy. 

IV. — Dimensions  of  bolt  heads. 

The  principal  requirements  of  the  head  of  a bolt  are  that  its  depth 
shall  be  such  as  to  prevent  the  bolt  from  pulling  out,  or  yielding  to 


26 


slieai'iyg  strains,  and  that  it  shall  afford  an  efficient  hold  for  the  wrench. 
These  requirements  are,  in  the  opinion  of  the  board,  as  well  answered 
by  Mr.  Seller’s  proportions  as  by  the  proportions  of  any  other  manu- 
factnrer  or  engineer,  and  hence  these  proportions  are  recommended. 

RECAPITULATION. 

In  order  to  prevent  confusion  we  present  here  the  entire  system 
recommended:  • 

nominal  diameter  of  bolt, 
pitch  of  thread, 
number  of  threads  per  inch, 
depth  of  nut. 

short  diameter  of  hexagonal  or  square  nut. 
effective  diameter  of  bolt  — diameter  under  root  of  tliread. 
depth  of  thread, 
depth  of  head, 
short  diameter  of  head. 


yj  ~ 0. 24  V JD  + 0.625  — 0.175 

N=1 

p. 

s 0.65  p. 

(Z=rD~2.S. 

rr  D — 1.3  p, 

H D. 

(Z.=  JD  + i". 

= 3 D + i". 

^>=|D  + tV 
/i  = D. 

■ The  following  table  (IV)  gives  the  results  obtained  by  the  use  of 
tliese  formulae  for  all  the  sizes  of  bolts.  The  only  instance  where  the 
values  in  the  table  differ  from  those  given  by  the  formulae  is  in  the 
numbers  of  threads  per  inch,  which  are  so  far  modified  as  to  use  the 
nearest  convenient  aliquot  part  of  a unit,  so  as  to  avoid,  as  far  as 
practicable,  troublesome  combinations  in  the  gear  of  screw-cutting 
machines. 


D = 

n — 


H = 


Then 


27 


Table  IV. — Proposed  standard  dimensions  of  holts  and  nuts  for  the  United 

States  navy. 


BOLT. 

NUT. 

HEAD. 

Diameter. 

j Threads 

per  inch. 

Short  diameter. 

Depth— H. 

Short  diam- 
eter— dn. 

Depth— 

Xominal— D 

i 

Effective— 

1 

^By  formu- 
la— ?i. 

Standard 

number. 

Hexagon — dn. 

Square — dn. 

J. 

.185 

20.  24 

20 

i 

i 

i 

i 

5-16 

.240 

17.  45 

18 

19-32 

19-32 

.ii6 

19-32 

19-64 

8. 

8 

.294 

15.  38 

16 

11-16 

11-16 

&. 

11-16 

11-32 

7-16 

..345 

13.  80 

14 

25-32 

25-32 

7-16 

25-32 

25-64 

J. 

.400 

12. 60 

13 

i- 

1 

i 

7-16 

y-16 

. 454 

11.55 

12 

31-32 

31-32 

9-16 

31-32 

31-64 

.507 

10.  72 

11 

1 1-16 

1 1-16 

f 

1 1-16 

17-32 

i 

.620 

9.  39 

10 

If 

11 

f 

11 

i 

1 

,731 

8.  40 

9 

1 7 16 

1 7-16 

1 

1 7-16 

23-32 

1 

.837 

7.  63 

8 

11 

If 

1 

11 

13-16 

U 

.940 

7.  02 

7 

1 13-16 

1 13-16 

n 

T 13-16 

39-32 

H 

1.065 

6.  50 

7 

o 

o 

11 

o 

1 

1! 

1.160 

6.  08 

6 

2 3-16 

2 .3-16 

If 

2 3-16 

1 3-32 

LV 

1.284 

5.  72 

6 

2-1 

21 

H 

2f 

1 3-16 

l| 

1.  .389 

5 41 

5^ 

2 9-16 

2 9-16 

11- 

2 9-16 

1 9-32 

If 

1.491 

5. 13 

5 

2f 

2f 

H 

21 

M 

U 

1.  616 

4.  90 

5 

2 15-16 

2 15-16 

H 

2 15-16 

1 15-32 

o 

1.712 

4,  67 

44- 

3i 

31 

2 

31 

1 9-16 

h 

1.  962 

4.31 

31 

31 

21 

31 

H 

2.  176 

4.  01 

4 

3| 

3| 

21 

31 

1 15-16 

2.  426 

3.  77 

4 

41 

41 

2f 

41 

21 

3 

2.  629 

3.56 

3i 

41 

4f 

3 

4f 

2 5-16 

3f 

2.  879 

3.36 

31 

5 

5 

31 

5 

21 

31 

3. 100 

3.  20 

3} 

5| 

51 

31 

of 

2 11-16 

3| 

3.317 

3.  06 

3 

5f 

5f 

3f 

5f 

21 

4 

3.  567 

2.93 

3 

6i 

6i 

4 

61 

3 1-16 

4i 

3.  798 

2.  82 

21 

61 

61 

41 

61 

31 

4i 

4.028 

2.  72 

2f 

6i 

6| 

41 

6| 

3 7-16 

4f 

4.  2.56 

2.  62 

2-1 

7-1 

71 

4f 

71 

3f 

5 

4.  480 

2.  54 

21 

7i 

7i 

5 

7f 

3 13-16 

5f 

4.730 

2.  46 

21 

8 

8 

51 

8 

4 

51 

4.  953 

2.  39 

21 

81 

51 

8f 

4 3-16 

5| 

5.  203 

2.  33 

2f 

8i 

5| 

8f 

4f 

6 

5.  423 

2.  26 

2.1: 

91 

91 

6 

91 

4 9-16 

COXCLUSIOX. 

Ill  conchidiiig  this  report  the  board  desires  to  say,  that  in  recom- 
mending the  system  of  Mr.  Sellers  as  a standard  for  the  navy,  it  has 
been  governed  by  considerations  other  than  those  suggested  by  tlie 
merits  inherent  in  the  system  itself. 

Fully  realizing  the  importance  of  entire  uniformity  of  practice  in 
private  establishments,  as  well  as  in  the  navy,  we  were  naturally 
desirous  to  select  a system  which,  while  meeting  all  the  essential  re" 
quirements  of  a system,  would  be  most  likely  to  be  generally  acquiesced 
in  and  adopted. 

So  far  as  we  have  been  able  to  confer  with  engineers  and  manufac- 
turers, either  personally  or  by  letter,  we  have  heard  but  one  opinion 
expressed  in  regard  to  the  importance  of  uniformity  of  practice. 
Many  liave  already  adopted  the  Sellers  pitcli;  others  are  graduall}- 
adopting  it,  while  others  still  express  their  willingness  to  adopt  it 


28 


A majority,  we  confidently  believe,  are  now  willing  to  adopt  Sellers’s 
form  of  thread  also,  provided  it  be  made  the  standard. 

As  a proper  auxiliary  we  suggest  the  importance  of  having  all 
necessary  guages  manufactured  by  a single  establishment,  as  by  that 
means  only  can  entire  uniformity  bt  secured. 

Finally,  the  board  would  respectfully  but  earnestly  urge  upon  the 
Bureau  the  importance  of  a carefully  conducted  series  of  experinaents 
upon  bolts  and  nuts,  with  a view  of  determining  the  precise  effect  of 
friction  between  their  rubbing  surfaces  under  varying  loads  and  under 
the  varying  conditions  of  actual  practice. 

We  have  the  honor  to  be,  very  respectfully,  your  obedient  servants, 

THEO.  ZELLER, 

Chief  Engineer  U.  S.  Navy. 
ALEXANDER  HENDERSON, 

Chief  Engineer  U.  S.  Navy. 

D.  M.  GREENE, 

First  AssH  Engineer  V,  S.  Navy. 

Chief  Engineer  B.  F.  Isherwood,  U.  S.  N., 

Chief  of  Bureau  of  Steam  Engineering. 


O 


9 


